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Author: Norihiro Kamide

Affiliation: Teikyo University, Japan

ISBN: 978-989-758-172-4

Keyword(s): Connexive Logic, Nelson’s Paraconsistent Logic, Duality, Sequent Calculus, Cut-elimination Theorem, Embedding Theorem.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Knowledge Representation and Reasoning ; Symbolic Systems

Abstract: Duality in constructive (or intuitionistic) logics is an important basic property since the dual counterpart of a given constructive logic can obtain a refutation or falsification of the information or knowledge which is described by the given logic. In this paper, duality in some intuitinistic paraconsistent logics is investigated. A constructive connexive logic (connexive logic for short) and Nelson’s paraconsistent four-valued logic are addressed as an example of such intuitionistic paraconsistent logics. A new logic called dual connexive logic (dCN), which is the dual counterpart of the connexive logic (CN), is introduced as a Gentzen-type sequent calculus. Some theorems for embedding dCN into CN and vice versa, which represent the duality between them, are shown. Similar embedding results cannot be shown for Nelson’s paraconsistent four-valued logic. But, similar embedding results can be shown for an extended Nelson logic with co-implication.

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Paper citation in several formats:
Kamide, N. (2016). Duality in Some Intuitionistic Paraconsistent Logics.In Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-172-4, pages 288-297. DOI: 10.5220/0005684202880297

@conference{icaart16,
author={Norihiro Kamide.},
title={Duality in Some Intuitionistic Paraconsistent Logics},
booktitle={Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2016},
pages={288-297},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005684202880297},
isbn={978-989-758-172-4},
}

TY - CONF

JO - Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Duality in Some Intuitionistic Paraconsistent Logics
SN - 978-989-758-172-4
AU - Kamide, N.
PY - 2016
SP - 288
EP - 297
DO - 10.5220/0005684202880297

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